from numpy import *
from numpy.polynomial import polynomial as poly

w_roots = range(1,21)
print w_roots # les racines du polynôme
w = poly.polyfromroots(w_roots)
print w # les coefficients du polynôme

roots(w[::-1])

w[19]

w_mod = w
w_mod[19] = -210.0 - 2**(-23)
print w_mod[19]

w_mod_roots = roots(w_mod[::-1])
w_mod_roots = w_mod_roots[::-1] 
print w_mod_roots

w_roots - w_mod_roots

print w_mod_roots[10], w_roots[10]